Showing papers in "Journal of Sound and Vibration in 1987"

Abstract: The coupling of longitudinal and bending vibrations of a rotating shaft, due to an open transverse surface crack is investigated. The assumption of the open crack leads to a system with behaviour similar to that of a rotor with dissimilar moments of inertia along two perpendicular directions. The local flexibility due to the presence of the crack can be represented by way of a 6×6 matrix for six degrees of freedom in a short shaft element which includes the crack. This matrix has off-diagonal terms which cause coupling along the directions which are indicated by these terms. Here shear is not considered and three degrees of freedom are used: bending in the two main directions and extension. This leads to a 3×3 stiffness matrix with coupling terms. The undamped free and forced coupled vibration are first considered. The coupling is investigated and the effects of unbalance and gravity are examined. Then damped coupled vibration is considered for free and forced vibration. The existence of coupling between longitudinal and bending vibration due to the crack is a very useful property which, together with the sub-critical resonance due to crack, can form a basis for crack identification in rotating shafts. New and interesting phenomena of coupled transverse and longitudinal motion are presented and discussed.

Abstract: An investigation of the localization phenomenon is presented for disrodered structural systems consisting of weakly coupled component systems. Emphasis is placed on the development of a perturbation method that allows one to obtain the localized modes of vibration of the disordered system from the modes of the individual subsystems. The principal feature of this perturbation method is that it not only considers the variations of the parameters as perturbations, but it also treats the small coupling between subsystems as a perturbation. Such a perturbation analysis is cost effective as compared to a global eigenvalue analysis of the entire system, and proves to be very accurate. Moreover, it provides physical insight into the localization phenomenon, and allows one to formulate a criterion that predicts the occurrence of strongly localized modes. Results are obtained for a chain of single-degree-of-freedom coupled oscillators, but these can be readilt generalized to deal with chains of multi-degree-of-freedom component systems.

Abstract: The likely character of the wavevector-frequency spectrum of turbulent wall pressure on a smooth rigid plane is reexamined Also, modeling is extended, for low Mach numbers, to the acoustic wavenumber domain From the relation of the wavevector-frequency amplitude of wall pressure to amplitudes of fluctuating vorticity-related velocity products (Reynolds stresses) regarded as its sources, the dependence of the wall-pressure spectrum at subconvective wavenumbers is seen to depend essentially on the rate of decrease of the source cross-spectra with wall distance (y) and on the identity of the wavenumber coefficient (eg, ω/v* or δ−1) that scales this profile A model wall-pressure spectrum proposed earlier is generalized with respect to this rate of decrease and found to permit a range of possible dependences between K0 and K2 in that part of the subconvective domain where K δ−1 If a contribution to the source spectrum exists that is roughly independent of wall distance for v*/ω y K−1, it may dominate the wall pressure in the subconvective range and lead for Kδ1 to wavenumber independence of the spectrum, in accord with the Martin-Leehey wind-tunnel measurement A comprehensive trial model for the wall-pressure spectrum based on source models yielding this character is proposed and viewed as potentially satisfactory in all wavenumber domains from the acoustic to the convective For ω/c K δ−1, it varies as K2, as follows for any source-spectral profile that decreases at least as (δ/y)4 for y δ, and accords with the Phillips-Kraichnan theorem

Abstract: A method based on the work of Tam and Tanna (1982) for calculating the near field noise spectrum and the spatial distribution of broadband shock associated noise from supersonic jets is proposed. Multiple-scales expansion is used to decompose the quasi-periodic shock cells into time-independent waveguide modes of the jet flow, and the interaction of the instability waves with each of the waveguide modes is shown to generate unsteady disturbances which become part of the broadband shock associated noise when radiated to the far field. The observed broadband shock associated noise is composed of a superposition of the various distinct spectra of the different waveguide modes, and the multispectra can be easily identified in many of the existing far and near field noise measurements.

Abstract: Transient dynamic analysis of flexible structures undergoing large motions is considered. For rotating structures, it is explicitly shown that appropriate account of the influence of centrifugal force on the bending stiffness requires the use of a geometrically non-linear (at least second-order) beam theory. Use of a first-order (linearized) linear beam theory results in a spurious loss of bending stiffness. For a rotating plane beam, a set of linear partial differential equations of motion—that includes all inertia effects (Coriolis, centrifugal, acceleration of revolution) and coupling between extensional and flexural deformations—is derived from the fully non-linear beam theory by consistent linearization. The analysis is subsequently extended to the more general case of a plate, accomodating shear deformation, and undergoing a general three-dimensional rotating motion. The discretization process of the resulting linear equations of motion for the beam and the plate is also discussed.

Abstract: The steady state, vibro-impacting responses of one dimensional, harmonically excited, linear oscillators are studied by using a modern dynamical systems approach allied with numerical simulation. The steady state motions are attracting sets in the system phase space and capture initial conditions in their domains of attraction. Unlike the free, harmonically excited oscillator, the phase space of a vibro-impacting system may be inhabited by many attracting sets. For example, there are sub-harmonic, multi-impact, periodic orbits and chaotic, steady state responses. In order to build a qualitative understanding of vibro-impact response, an attempt is made to build generic topological models of their phase spaces for physically significant parameter ranges. Use is made of the Poincare section or stroboscopic mapping technique, essentially following an initial impact forwards or backwards in time to subsequent or previous impacts using a computer. The qualitative understanding gained from the analysis and simulations is discussed in an engineering context.

Abstract: An analysis is presented of the effectiveness with which active methods can be used for producing global reductions in the amplitude of the pressure fluctuations in a harmonically excited enclosed sound field. The total time averaged acoustic potential energy is expressed as a quadratic function of the complex strengths of a number of secondary sources of sound introduced into the enclosure. For a given number and location of secondary sources, there is a unique set of source strengths which determines the minimum value of this function. The analysis is applied to the case of a lightly damped enclosure excited by a point primary source at a frequency above the Schroeder cut-off frequency. It is demonstrated that substantial reductions in the total time averaged acoustic potential energy are possible only if the secondary sources of sound are located at a distance from the primary source which is less than half a wavelength at the frequency of interest.

Abstract: The dry and wet dynamic characteristics of a vertical and a horizontal cantilever square plate [1] immersed in fluid are discussed from the viewpoint of a linear hydroelasticity theory [2–5]. The surface piercing vertical plate is partially immersed in the fluid and the influence of submerged plate length on the resonance frequencies investigated. For the horizontal plate the influence of submerged depth below the free surface on the resonance frequencies is examined. Incorporated into the theoretical model is a free surface boundary condition allowing wave disturbances to be present. The interaction existing between the vibrating cantilever plate and the free surface is clearly exhibited in the calculated curves describing the generalized hydrodynamic coefficients. A limited comparison between predictions and experimental data [1] is also included.

Abstract: The vibration of rotating rings is investigated. The equations of motion that cover both transverse and tangential motion are derived from Hamilton's principle. The natural frequencies and modes are then obtained without using the inextensional assumption and an attempt is made to interpret the time dependent natural modes from various viewpoints. The effect of rotation and elastic foundation on system characteristics is examined. Most important, a general solution for forced vibration is formulated and demonstrated by an example. The effect of the Coriolis acceleration component on the forced response is illustrated by comparing the results for a travelling force on a stationary ring with results for a rotating ring subjected to a stationary force.

Abstract: Sound generation by vortex pairing in circular and elliptic cold-air jets at Mach 015-035 is investigated experimentally, with a focus on the effects of initial conditions The results are presented in graphs and interpreted using the theory of vortex sound proposed by Moehring (1978) and vortex-filament models of jet coherent structure Tripping the nozzle boundary layer is shown to (1) preempt formation of shear-layer vortices, (2) remove the sound they produce in later pairing, and (3) increase the diffusion of coherent vorticity in the vortex rings Hence pairing noise should not be significant in practical jets, which are initially turbulent

Abstract: The problem of the non-linear dynamics of rotor/casing rub interactions in rotating equipment is investigated. Specifically, a non-linear analytical rotor casing rub interaction simulation is solved. This yields insights as to the interrelationship between rub force histories, energy levels, rub duration, incidence separation angles, and backward whirl initiation, as well as the overall rotor orbit during successive rubs. Special attention is also given to determine the effects of casing stiffness, friction coefficient, imbalance load and system damping characteristics.

Abstract: Optimization techniques are used to enable an unambiguous quantification of the degree to which the sound power output of a distribution of point primary sources can be reduced by the addition of a number of point secondary sources. The near field technique developed by Levine is used to calculate the total power output from an arbitrary number of point primary and secondary sources. This power output is a quadratic function of the complex strengths of the secondary point sources. For a given arrangement of primary and secondary sources, this quadratic function has a unique minimum value associated with an optimal set of secondary source complex strengths. Results are presented for the minimum power radiated by the combination of a single point primary source and various arrangements and numbers of point secondary sources. In particular it is demonstrated that, for the number of secondary sources considered, substantial reductions in total power output can be achieved only if the secondary sources are separated from the primary source by a distance which is less than one half wavelength at the frequency of interest. It is possible, however, to produce net source distributions of unexpectedly low radiation efficiency with a relatively small number of secondary sources placed close to the primary source.

Abstract: This paper is Part II in a series of three papers on the active minimization of harmonic enclosed sound fields. In Part I it was shown that in order to achieve appreciable reductions in the total time averaged acoustic potential energy, Ep, in an enclosed sound field of high modal density then the primary and secondary sources must be separated by less than one half wavelength, even when a relatively large number of secondary sources are used. In this report the same theoretical basis is used to investigate the application of active control to sound fields of low modal density. By the use of a computer model of a shallow rectangular enclosure it is demonstrated that whilst the reductions in Ep which can be achieved are still critically dependent on the source locations, the criteria governing the levels of reduction are somewhat different. In particular it is shown that for a lightly damped sound field of low modal density substantial reductions in Ep can be achieved by using a single secondary source placed greater than half a wavelength from the primary source, provided that the source is placed at a maximum of the primary sound field. The problems of applying this idealized form of active noise control are then discussed, and a more practical method is presented. This involves the sampling of the sound field at a number of discrete sensor locations, and then minimizing the sum of the squared pressures at these locations. Again by use of the computer model of a shallow rectangular enclosure, the effects of the number of sensors and of the locations of these sensors are investigated. It is demonstrated that when a single mode dominates the response near optimal reductions in Ep can be achieved by minimizing the pressure at a single sensor, provided the sensor is at a maximum of the primary sound field. When two or three modes dominate the response it is found that if only a limited number of sensors are available then minimizing the sum of the squared pressures in the corners of the enclosure gives the best reductions in Ep. The reasons for this behaviour are discussed.

Abstract: This paper presents an exact determination of coupled bending and torsion vibration characteristics of uniform beams having single cross-sectional symmetry. A novel feature of the analysis is the expression of the exact solutions in terms of real functions, as is usual in more elementary vibration problems of beams. Numerical results are given to explain the effect of the shear centre offset on the natural frequencies.

Abstract: The feasibility of reducing interior noise caused by advanced turbo propellers by controlling the vibration of aircraft fuselages was investigated by performing experiments in an anechoic chamber with an aircraft model test rig and apparatus. It was found that active vibration control provides reasonable global attenuation of interior noise levels for the cases of resonant (at 576 Hz) and forced (at 708 Hz) system response. The controlling mechanism behind the effect is structural-acoustic coupling between the shell and the contained field, termed interface modal filtering.

Abstract: The variational method of Schwinger is applied to reach qualitative conclusions regarding the effects of symmetrical discontinuities (change in cross-section, diaphragm of zero thickness) in acoustic waveguides. For bidimensional geometry the exact results from an analytical solution are used to discuss the convergence of the solutions of the modal theory when the number of modes taken into account increases. The variation of the discontinuity inductances with frequency and the difference between radiation into infinite space and into a large waveguide are discussed. Finally, by a fitting procedure a set of formulae is provided for the engineer for both the case of the radiation of a plane piston into an infinite waveguide and the case of a change in cross-section in a circular guide.

Abstract: The vibration in a flexible robot arm modeled by a moving slender prismatic beam is considered. It is found that the extending and contracting motions have destabilizing and stabilizing effects on the vibratory motions, respectively. The vibration analysis is based on a Galerkin approximation with time-dependent basis functions. Typical numerical results are presented to illustrate the qualitative features of vibrations.

Abstract: An introductory, theoretical study for characterization of structural acoustic sources has been carried out. The concept source denotes any active structure with unknown internal elementary source mechanisms and unknown internal transmission paths from generation to the contact points with the receiving structure. An alternative description of the power transmission from the source to the receiver is presented in the case of one component of motion and one contact point. A general source parameter called the source descriptor is introduced. This parameter is a function of source data only. It is proportional to power and involves both the internal vibration of the source and its mobility at the contact point. From experimental measurement series, it can be emphasized that the velocity of the free source is a suitable and manageable quantity for describing the internal vibration of many structure-borne sound sources. The active power transmitted from the source structure to the receiving one is found to be the product of the source descriptor and a dimensionless function called the coupling function. This function illustrates the dynamic properties of the source-receiver interface.

Abstract: A set of characteristic orthogonal polynomials in two variables is used as deflection functions to obtain the natural frequencies and mode shapes of polygonal plates by the Rayleigh-Ritz method. The set of orthogonal polynomials is constructed by employing the Gram-Schmidt orthogonalization procedure. The first six natural frequencies are numerically evaluated for triangular plates of different configurations by using these orthogonal functions and the corresponding mode shapes are plotted. Results are compared with those obtained previously by other methods.

Abstract: The theory is developed for obtaining the propagation constants of a thin uniform cylindrical shell, periodically stiffened by uniform circular frames of general cross-section. The free wave motion is analyzed and the stop and pass bands of free wave motion in the structure are located. Hysteretic damping is included. The natural frequencies of two stiffened finite cylindrical shells are deduced. The relative effects of the frame cross section and pitch on the free vibration characteristics of the whole structure are discussed.

Abstract: Sullivan and Crocker's equations for two-duct perforated elements were solved recently by Jayaraman and Yam by means of a decoupling approach, which was valid only for equal mean-flow Mach numbers in the two interacting ducts. The present paper provides a generalized decoupling approach for the analysis of two-duct as well as three-duct muffler configurations consisting of perforated elements, taking into account the actual mean flow Mach numbers in the adjoining tubes. The theoretical results of transmission loss of typical muffler configurations are compared with the available measurements of Sullivan, and predictions of Jayarman, Yam and Thawani. A comparison has been made with the TL values calculated by means of Sullivan's segmentation approach. The agreement between the two seems to be good.

Abstract: A cable dynamics theory is derived for travelling cables having arbitrary initial sag and arbitrary support eyelet elevations. The theory incorporates the effect of cable elasticity through a finite strain model. Hamilton's principle provides three non-linear equations which describe the three-dimensional motion of the cable. The equations are linearized about a known equilibrium configuration. Natural frequencies, mode shapes and stability of equilibrium are predicted from the eigensolutions of the discretized model over a range of cable designs. Results of previous elastic cable theories are re-examined and new findings are presented.

Abstract: The active control of disturbances propagating along a waveguide is considered with particular reference to the control of flexural vibrations in thin beams. The control system consists of a number of point sensors and point exciters distributed in some manner along the waveguide. The sensor measurements are used as inputs to a controller which forms the required excitations such that incoming disturbances are completely cancelled. A method by which this ideal controller can be synthesized is presented. The stability of the system is considered. In general the system reflects the downstream cancelled disturbances while upstream disturbances are both reflected and transmitted. Active control of flexural waves in beams is then considered and two possible active control systems are examined. The first consists of measurements of displacement and rotation at a point and the application of a point force and point moment while the second comprises displacement measurements at two points and the application of two point forces. In both cases the ideal active controller is derived and some aspects of the systems' performances examined.

Abstract: The influence of fluid-containing appendages on the dynamic response of multi-degree-of-freedom systems subjected to stochastic environmental loads, e.g., earthquakes, waves, or winds, is investigated. The modal properties of a system comprising of a fluid-containing appendage attached to a multi-degree-of-freedom system are expressed in terms of the individual dynamic properties of the primary and secondary systems. The primary system is modeled as a lumped mass multi-degree-of-freedom system. An equivalent lumped mass model of the sloshing fluid is used to represent the secondary system. All the frequencies of the secondary system that are less than or equal to the fundamental natural frequency of the primary system are included in the dynamic analysis of the combined system. The input to the system may be a stationary or a non-stationary white or filtered white noise vector-valued excitation. In this study the structural response to an earthquake represented by a non-stationary filtered white noise is computed at any time interval by utilizing the modal impulse-response function and approximating the envelope intensity function with a staircase unit impulse function. The formulation presented here renders the computational procedure very efficient by reducing the multiplicity of the integrals. The covariance matrices of the response components of the combined system are computed by using this formulation. The peak response values at any level on the structure may be obtained by following the evolutionary distribution of the extreme values. An important feature of the combined system is that the response of the primary system is suppressed when one of the sloshing modes of the secondary fluid appendage is tuned to the fundamental mode of the primary system. A building with a water tank situated at any floor, excited by an earthquake, is used to illustrate the methodology.

Abstract: The intent of this study is (i) to analyze the response of a rotating disc, clamped at the inside and free at the perimeter, subjected to excitation produced by stationary point loads and restrained by stationary point springs and (ii) to investigate the effect of spring stiffness, number of spring and spring location on the frequency speed characteristics of the rotating disc The purpose of this work is to develop fundamental understanding of the dynamics of guided rotating discs and to apply this knowledge to the analysis and design of guided circular saws used in the sawmilling industry

Abstract: A review of the current state of knowledge of wheel/rail squeal and impact noise is presented. Mechanisms for noise generation, sources of noise, predictive models and means for control are presented. Areas where additional research is required are suggested. While considerable progress in expanding our understanding of wheel/rail noise has occurred in the past ten years, there are still many areas of controversy and many areas where firmly based scientific information is lacking.

Abstract: Strain gauge measurements made on an impacted plate have been used to infer the contact force history. Experimental results for the impact of a scotchply laminated composite are presented.

Abstract: The differential system characterization of hysteretic system is well known The problem of estimating the parameters of this system on the basis of input-output data, possibly noise corrupted, is considered It turns out that the estimation problem is a non-linear optimization problem The Gauss Newton method is used in setting up a two-stage iterative least squares algorithm The usefulness of the algorithm is validated through its application to various simulated time histories from the hysteretic model

Abstract: Radiated noise generated by a high-speed electric train travelling at speeds up to 250 km/h has been measured with a line array of microphones mounted along the wayside in two different orientations. The test train comprised a 103 electric locomotive, four Intercity coaches, and a dynamo coach. Some of the wheels were fitted with experimental wheel-noise absorbers. By using the directional capabilities of the array, the locations of the dominant sources of wheel/rail radiated noise were identified on the wheels. For conventional wheels, these sources lie near or on the rim at an average height of about 0·2 m above the railhead. The effect of wheel-noise absorbers and freshly turned treads on radiated noise were also investigated.